Descriptive-complexity conjecture for nondeterministic dynamically generated basic sequences
Descriptive-complexity conjecture for nondeterministic dynamically generated basic sequences
Let be a nondeterministic dynamically generated basic sequence. Let , , and denote the corresponding normality classes, and let denote the stated difference-hierarchy completeness class. Descriptive-complexity conjecture. The following sets each have Hausdorff dimension and are -complete:
- ;
- ;
- .
This is proposed as a strong converse direction to the deterministic normality-equivalence conjecture, predicting both maximal Hausdorff dimension and precise descriptive complexity.
Sources & referencesView supporting material
Primary source
Sohail Farhangi and Bill Mance, “The Theory of Normality for Dynamically Generated Cantor Series Expansions”, arXiv:2512.01239 (2025).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.